Calculus of Variations and Geometric Measure Theory

S. Almi - G. Lazzaroni - I. Lucardesi

Crack growth by vanishing viscosity in planar elasticity

created by lazzaroni on 05 Jun 2019
modified on 09 Mar 2022


Published Paper

Inserted: 5 jun 2019
Last Updated: 9 mar 2022

Journal: Mathematics in Engineering
Volume: 2
Number: 1
Pages: 141-173
Year: 2020
Doi: 10.3934/mine.2020008

ArXiv: 1906.02631 PDF
Links: Journal website


We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of (unions of) regular curves. To prove the result, it is crucial to analyze the properties of the energy release rate.